1. Field of the Invention
The present invention relates to a method and a device for real-time separation of mixed signals.
2. Discussion of the Related Art
The problem posed is the blind identification of a mixture of signals. Signals are received on a certain number of sensors, equal to p in number for example. These signals come from a mixture, which is by assumption linear but whose transfer function is unknown, of a number n less than or equal to p of "source" signals which are also unknown, and which, also by assumption, come from independent and non-Gaussian (except strictly for one of them alone) sources. It therefore involves at the same time separating, that is to say identifying, these source signals and determining the transfer function effecting the mixture of signal which are received on the p abovementioned sensors: it is therefore a problem of blind deconvolution.
Taking the simple example from the field of radar of sonar, the signals received by the sensors which together constitute the reception antenna, are generally processed to form channels in directions chosen a priori, this making it possible to spatially separate "sources" constituted by echoes or noise-makers. The problem posed here is to identify there channels directly.
Thus, to fix ideas, if two sources x.sub.1 (t) and x.sub.2 (t), where t is the time variable, and two sensors providing two signals e.sub.1 (t) and e.sub.2 (t) such that: EQU e.sub.1 (t)=x.sub.1 (t)+.beta.x.sub.2 (t) EQU e.sub.2 (t)=.alpha.x.sub.1 (t)+x.sub.2 (t)
are considered, if it is then possible to obtain .alpha. and .beta., that is to say to identify the transform matrix: ##EQU1## the two channels EQU e.sub.1 (t)-.beta.e.sub.2 (t) EQU and e.sub.2 (t)-.alpha.e.sub.1 (t)
are available which effect the desired separation of the source signals x.sub.1 (t) and x.sub.2 (t).
In this example, the source signals are taken at the same instant t: the mixture of signals is termed "instantaneous". In general, mixtures are not instantaneous but "convolutive". It is nevertheless possible to reduce a convolutive problem to an instantaneous problem by decomposing the signals into signals with pure frequencies by spectral analysis obtained by FOURIER Transformation. Denoting the frequency by f, each observed signal can then be written: ##EQU2## and each source signal can be written: ##EQU3## Finally, the blind deconvolution problem to be solved here can be stated thus:
p signals (p greater than or equal to 2) are observed, and for which it is known that they arise from n unknown source signals (n less than or equal to p) through an unknown linear, stationary transformation A(f) such that: ##EQU4## the signals e(t), x(t) and the transformation A possibly being complex data. Moreover, independent and, except strictly for one of them along, non-Gaussian sources are involved. Blind deconvolution then consists in the determination of the transfer function A and thereby of each of the source-signals.
A known solution for effecting a time separation of an instantaneous mixture A(f)=A of signals is proposed by Messrs. C. JUTTEN and J. HERAULT in several articles including the one published in the French journal "Traitement du Signal", volume 5, No. 6, 1988, pages 389 to 403. In involves a method of separation which uses a fully interconnected signal-layer array of linear neurons whose weights are supervised by an algorithm akin to that of stochastic iteration.
This known method nevertheless has some disadvantages:
the algorithm used does not always converge, and it may therefore provide erroneous outputs, which would diverge if there were no natural saturation; PA1 when there is convergence, the speed of convergence of this algorithm can be extremely slow; PA1 whether or not convergence occurs depends on the initialization, as well as on the speed of convergence and on the solution provided. PA1 a first step of obtaining, in a manner known per se, p decorrelated signals s(t) from these received signals e(t); and PA1 a second step of calculating an orthogonal matrix Q such that x(t)=Q s(t), x(t) being the required source-signals, this orthogonal matrix Q, which effects a linear transformation, being obtained from polynomial transformations of the data with the aid of polynomials of degree 3 or 4, and being determined, with the aid of a stochastic algorithm which stores average statistics called moments and cumulants, and which then uses these estimated moments and cumulants to effect the real-time determination of the matrix Q.